Page:LewisRevision.djvu/7

Rh Its momentum and kinetic energy will change according to (11) and (12) by the amounts

Hence

So far the equations are those of Newtonian mechanics, but now in substituting for M from equation (10) we must regard m as a variable and write

This will be our fundamental equation connecting the kinetic energy of a body with its mass and velocity.

Introducing now the relation of mass to energy given in equation (7) we may write,

and combining this equation with (14) gives

This equation, containing only two variables, m and v and the constant V, may readily be integrated as follows. By a simple transformation

Writing &beta;=v/V, and noting that

we see that

Hence

where log m0 is the integration constant. Therefore

or

This is the general expression for the mass of a moving body in terms of &beta;, the ratio of its velocity to the velocity of